Skriniar is set to become a free agent at the end of this season and has been strongly linked with a move to Paris Saint Germain.
Inter held transfer discussions with PSG over Skriniar last summer but a move never materialised before Simone Inzaghi's side came forward with fresh terms later.
But Skriniar's agent, Roberto Sistici, has described Inter's offer as inadequate and has already held talks with foreign clubs regarding a summer move.
"The truth is that the decision to place Milan Skriniar on the transfer market in the summer was made by Inter, obviously not by the player," Sistici told TeleNord.
"It was a choice by the club that led to a negotiation between Inter and PSG, of which we had obviously been informed. At a certain point, the negotiation broke down, and we had also been informed of this step, a decision that was not up to us and which the player accepted calmly, with professionalism and absolute respect for the contract.
"Last autumn, we responded to all the meeting requests made by the club. After a series of preliminary meetings, we presented our financial request and subsequently, at the beginning of November 2022, the club presented us with a proposal.
"About a month later, before Christmas, I communicated to Inter the decision not to accept their offer, a choice reiterated at the beginning of January, before the Supercoppa, when I also informed the managers [Giuseppe] Marotta and [Piero] Ausilio that we thought we were free to listen to offers from other clubs.
"Maybe it wasn't mandatory communication, but for the player and myself it was the most correct way to proceed, knowing that seriousness and transparency are the best way to proceed for us. I repeat, we have never missed any appointment with Inter."
He added: "We didn't talk about PSG, just as we didn't leak our and Inter's positions, given that with Inter we had agreed to handle the matter with the right confidentiality, in the interest of serenity and the performance of the team and of the player.
"There are contacts with some clubs. Not Italian [clubs]."
Skriniar has won one Serie A, one Coppa Italia and two Italian Super Cups since joining Inter from Sampdoria in 2017.
